A quadrature rule for finite-part integrals

A quadrature rule is described for evaluating finite-part (f.p.) integrals of the form , witha 1. The rule is obtained by interpolating tof by a polynomial which coincides withf at the shifted zeros of a Legendre polynomial.     

Clean reconstructed InAs(1 1 1) A and B surfaces using chemical treatments and annealing

Well-ordered clean InAs(1 1 1) A and B surfaces have been prepared using HCl-isopropanol solutions and characterized using low-energy electron diffraction and photoemission spectroscopy. The as-treated surfaces are covered by a layer containing arsenic and small amounts of InCl_x. Annealing induces desorption of the overlayer and reveals (2 × 2) and (1 × 1) structures on the A and B surfaces, respectively. For both surfaces, the surface components of the In 4d and As 3d reveal a charge transfer from the electropositive surface indium to the electronegative surface arsenic. The major advantage of this preparation method over conventional thermal cleaning is a significant reduction in the annealing temperature (≈250 °C) thereby avoiding anion evaporation.     

An algorithm for the numerical evaluation of certain Cauchy principal value integrals

Summary An algorithm is described for numerically evaluating Cauchy principal value (c.p.v.) integrals of the type. The remainder is expressed as a contour integral, from which realistic asymptotic estimates are obtained.     

Young modules and filtration multiplicities for Brauer algebras

We define permutation modules and Young modules for the Brauer algebra B _k (r,δ), and show that if the characteristic of the field k is neither 2 nor 3 then every permutation module is a sum of Young modules, respecting an ordering condition similar to that for symmetric groups. Moreover, we determine precisely in which cases cell module filtration multiplicities are well-defined, as done by Hemmer and Nakano for symmetric groups. Supported by the European Community through Marie Curie fellowship MCFI 2002-01325 Supported by EPSRC grant GR/S18151/01     

Chemically prepared well-ordered InP(0 0 1) surfaces

In the present work HCl-isopropanol treated and vacuum annealed InP(0 0 1) surfaces were studied by means of low-energy electron diffraction (LEED), soft X-ray photoemission (SXPS), and reflectance anisotropy (RAS) spectroscopies. The treatment removes the natural oxide and leaves on the surface a physisorbed overlayer containing InCl_x and phosphorus. Annealing at 230 °C induces desorption of InCl_x overlayer and reveals a P-rich (2 × 1) surface. Subsequent annealing at higher temperature induces In-rich (2 × 4) surface. The structural properties of chemically prepared InP(0 0 1) surfaces were found to be similar to those obtained by decapping of As/P-capped epitaxial layers.     

Crystal and molecular structure of diphenylphosphinylacetic acid

Diphenylphosphinylacetic acid crystallizes in the monoclinic space groupP2_l/n with unit cell dimensionsa=5.6875(7),b=17.049(4),c=13.471(2) Å, =93.36(1)° and Z=4. The molecular packing consists of hydrogen bonded chains arising from intermolecular interactions between a carboxylic acid hydroxyl group and an oxygen of an adjacent phosphine oxide moiety.     

Cohomological stratification of diagram algebras

The class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras. While the definition is in combinatorial terms, by adding extra structure to Graham and Lehrer’s definition of cellular algebras, various structural properties are established in terms of exact functors and stratifications of derived categories. The stratifications relate ‘large’ algebras such as Brauer algebras to ‘smaller’ ones such as group algebras of symmetric groups. Among the applications are relative equivalences of categories extending those found by Hemmer and Nakano and by Hartmann and Paget, as well as identities between decomposition numbers and cohomology groups of ‘large’ and ‘small’ algebras.